{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "913db396-b7f9-4408-bdbf-793141e22740",
   "metadata": {},
   "source": [
    "Chapter 20\n",
    "# 三种天气状况\n",
    "Book_6《数据有道》 | 鸢尾花书：从加减乘除到机器学习"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ac25a39f-96d6-4b76-ac00-ebb77daa146d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3f210e47-a40c-451e-b9be-823c540c6716",
   "metadata": {},
   "outputs": [],
   "source": [
    "T = np.matrix([[0.7, 0.45, 0.55],\n",
    "               [0.25, 0.3,  0.3],\n",
    "               [0.05, 0.25, 0.15 ]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "921dca91-0bb9-4de3-966e-335259201737",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Sun', 'Sun'),\n",
       " ('Sun', 'Cloud'),\n",
       " ('Sun', 'Rain'),\n",
       " ('Cloud', 'Sun'),\n",
       " ('Cloud', 'Cloud'),\n",
       " ('Cloud', 'Rain'),\n",
       " ('Rain', 'Sun'),\n",
       " ('Rain', 'Cloud'),\n",
       " ('Rain', 'Rain')]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = T.T\n",
    "# 使用邻接矩阵创建有向图\n",
    "G = nx.from_numpy_array(A, create_using=nx.DiGraph)\n",
    "\n",
    "# 修改节点名称\n",
    "G = nx.relabel_nodes(G, {0: 'Sun', 1: 'Cloud', 2: 'Rain'})\n",
    "\n",
    "list(G.edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "77dc735c-e88a-4c3c-bd31-e48ad60d5971",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{('Sun', 'Sun'): Text(0.16924220867218978, 1.0, '0.7'),\n",
       " ('Sun', 'Cloud'): Text(0.35148726469266034, 0.3040335642072239, '0.25'),\n",
       " ('Sun', 'Rain'): Text(-0.26686616035656524, 0.19596643579277612, '0.05'),\n",
       " ('Cloud', 'Sun'): Text(0.35148726469266034, 0.3040335642072239, '0.45'),\n",
       " ('Cloud', 'Cloud'): Text(0.5337323207131309, -0.39193287158555223, '0.3'),\n",
       " ('Cloud', 'Rain'): Text(-0.08462110433609465, -0.5, '0.25'),\n",
       " ('Rain', 'Sun'): Text(-0.26686616035656524, 0.19596643579277612, '0.55'),\n",
       " ('Rain', 'Cloud'): Text(-0.08462110433609465, -0.5, '0.3'),\n",
       " ('Rain', 'Rain'): Text(-0.7029745293853202, -0.6080671284144478, '0.15')}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (6,6))\n",
    "pos = nx.spring_layout(G,seed=8)\n",
    "nx.draw_networkx(G, \n",
    "                 pos = pos,\n",
    "                 node_size = 180)\n",
    "\n",
    "edge_labels = nx.get_edge_attributes(G, 'weight')\n",
    "nx.draw_networkx_edge_labels(G, pos, \n",
    "                             edge_labels=edge_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b382bf2b-b7bb-4e4a-a883-49450071af87",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.61538462]\n",
      " [0.26923077]\n",
      " [0.11538462]]\n"
     ]
    }
   ],
   "source": [
    "# 稳态\n",
    "sstate = np.linalg.eig(T)[1][:,0]\n",
    "sstate = sstate/sstate.sum()\n",
    "print(sstate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "73a64bde-3326-4b59-a896-5b545db5c3f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# initial states\n",
    "initial_x_3 = np.array([[1, 0, 0],\n",
    "                        [0, 1, 0],\n",
    "                        [0, 0, 1]])\n",
    "\n",
    "num_iterations = 10;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0c8d233a-36be-44cd-8301-ab0af3ff6596",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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P8vJyZGdn17neJbuB8YXABS2B9f+vHk+UanXq1CkAQJMmTXSuhADmIQmzkINZyHHo0CGcd9559f7/XRvdeoBatGgBk8mEkpKSateXlJSgdevWMe8zbdo03HbbbbjzzjsBAH369IHT6cQvf/lLPPbYYzAaaw5p0ur8bXgm2LcnAH8IsOg+fy75hRumfGGRgXnIwSzkYBZy+Hw+TY+n279xq9WKQYMGobCwMHJdKBRCYWFhtR6haC6Xq0YjJ3yOMN4dWZ2zgSYWwBtUZ4NR42VkZGi+tDk1HPOQg1nIwSzkcDgcmh5P15WgJ0+ejAkTJmDw4MEYMmQIFixYAKfTiYkTJwIAbr/9drRr1w5z584FAIwdOxbz58/HgAEDIqfApk2bhrFjx0YaQvFiNAD9mgOfF6sLIvbJjevDpYXw4mJ8cZGBecjBLORgFnKk1FYY48ePx7FjxzB9+nQUFxejf//+WLFiRWRgdFFRUbUen8cffxwGgwGPP/44Dh06hJYtW2Ls2LF44oknElLvgKgG0O3dEvKQKY2Li8nCPORgFnIwCzm0XghRt0HQeqmoqEBOTk6DBlH9fRfwizXApW2A1WPjVGAaCS942apVK50rIYB5SMIs5GAWcuzevRtdunRJ/kHQySi8J9im44CiAAaDvvUkO76zkoV5yMEs5GAWcqTUVhjJpmczwGoEyn3A3lN6V5P8nE6n5ud0qeGYhxzMQg5mIYfWW5KwAVQPFiPQu2rwM3eGbzyHw6H5qH5qOOYhB7OQg1nIYbfbNT0eG0D1FN4YlTvDN57f74ff79e7DKrCPORgFnIwCzm0zoENoHoKL4jIHqDGMxgMMHAglRjMQw5mIQezkEPrHDgIup7YA6SdWCt3k36YhxzMQg5mIYfWWbABVE99mwMGAEdcQIkLyOPaWA3GbmVZmIcczEIOZiFHIBDQ9Hhs2tZTlgXolqNeZi9Q43BwoSzMQw5mIQezkIODoAXgOCBtVFZWRpaZJ/0xDzmYhRzMQo6U2gojWQ1oDryxG9jIBlCjcIExWZiHHMxCDmYhh9YLIbIB1ACRHiCeAmsUbjIoC/OQg1nIwSzkYA+QAOEG0O4KdVXoHKu+9SQrvrOShXnIwSzkYBZycCsMAVrYgfOqctjMXqAG47l1WZiHHMxCDmYhB3uAhBjYAjjoVAdC/6iN3tUkJ61b89Q4zEMOZiEHs5BD69OQ7AFqIC6I2Hherxder1fvMqgK85CDWcjBLOTQOgf2ADUQp8I3nslk0rsEisI85GAWcjALObTOgj1ADRRuAG0/CXiD+tZCRERE9cMGUAPlZwK5NiCgAFtP6F1NcgoGgwgG2XqUgnnIwSzkYBZyaJ0DG0ANZDBwPaDGstlssNlsepdBVZiHHMxCDmYhh9Y5sAHUCJGB0BwH1CBOp1PzaY3UcMxDDmYhB7OQw+VyaXo8DoJuBPYANQ4XGJOFecjBLORgFnJwKwxBwj1Am48DwRBgYn9avXCJeVmYhxzMQg5mIQcXQhSkWw6QYQZcAeC7cqBHM70rSi58ZyUL85CDWcjBLOTgVhiCmIxA31z1Mk+D1R+XmJeFecjBLORgFnJo3QPEBlAjcUHEhsvKyuK7K0GYhxzMQg5mIQd7gIQZyIHQDeZ2u+F2u/Uug6owDzmYhRzMQg6Px6Pp8TgGqJGip8Iriro+ENWNxWLRuwSKwjzkYBZyMAs5zGZtmyzsAWqk3rmA2QCc8AIHuFREvSiKAkVR9C6DqjAPOZiFHMxCDq1zYAOokWwmoGfV7C+OA6qfUCiEUCikdxlUhXnIwSzkYBZyaJ0DG0Aa4EDohrFYLOxeFoR5yMEs5GAWcmidAxtAGoiMA+JA6Hrh4EJZmIcczEIOZiEHB0ELxB6ghtF6SiM1DvOQg1nIwSzk0Ho1bvYAaaB/VQ/QASdwXNsGakrjAmOyMA85mIUczEIOLoQoULYV6JytXmYvUN1xgTFZmIcczEIOZiEHF0IUKjwOaCMbQHXGd1ayMA85mIUczEIOboYq1IAWwH/2ciB0ffBdlSzMQw5mIQezkIM9QEJFrwhNdeNyueByufQug6owDzmYhRzMQg6tZ+OxB0gj4Zlg35UDlX4gi8tGnJPNZtO7BIrCPORgFnIwCzmsVqumx2MPkEZaZwBtMgAFwLc8DVYnwWAQwWBQ7zKoCvOQg1nIwSzk0DoHNoA0xAURiYiIkgMbQBrigoj1YzKZYDKZ9C6DqjAPOZiFHMxCDq1zYANIQ+wBqh+v1wuv16t3GVSFecjBLORgFnL4fD5Nj8dB0BoK9wBtPQH4Q4CFzcuz0npZc2oc5iEHs5CDWcjhcDg0PR7/RWuoYxMgxwr4QsD2k3pXIx8XGJOFecjBLORgFnJwKwzBDIbT+4JxHNC5cYl5WZiHHMxCDmYhBxdCFI7jgOqO76xkYR5yMAs5mIUc3ApDOM4Eqzu+q5KFecjBLORgFnJo3QPEBpDGIg2g40BIAYwGfeuRLNya5yBDGZiHHMxCDmYhh9ZbkrABpLHuTQGbSd0OY3cF0DVH74rk0npEPzUO85CDWcjBLOSw2+2aHo9jgDRmMQJ9ctXLPA12dn6/H36/X+8yqArzkINZyMEs5NA6BzaA4mAgB0LXidFohNHIX0EpmIcczEIOZiGH1jnwFFgccCB03RgMHCAlCfOQg1nIwSzk0DoLNoDiIHogtKKo6wNRTexWloV5yMEs5GAWcgQCAU2PxwZQHPTJVWd/HXUDR1xAW21n7qUMDi6UhXnIwSzkYBZycBB0Esgwq7PBAI4DOhsuMCYL85CDWcjBLOTgVhhJYgC3xDgnLjEvC/OQg1nIwSzk4FYYSYIDoc+N76xkYR5yMAs5mIUc3AojSXBPsHPjuypZkjaPmTMBkwmYNq3m9+bMAYJB9TbSRT2PGlkky/NgFrKkQh5Rz4E9QEkivCv83lNAmVffWqTiOysBZs5UXwgRI485c+S/OALqi+P06ZHnETFnjnq9yaRPXfUV9TyqZZFMz4NZyJIKeUQ9B617gKCkmfLycgWAUl5eHvfH6vBvRcFfFeXTQ3F/qKRUWVmpVFZW6l1Gw8yYoSizZ8f+3uzZ6veTwezZigIoyuzZ1fOIuj4pnFlvstUfVlW39/HH1SyS8XkwC1lSIY+qmo899JCm/78NiqIo2japZKuoqEBOTg7Ky8uRnZ0d18f6fx8DS/cBz14ITO4b14dKSidOnAAA5Obm6lxJA4TfQc2eXb17ubbrEykUArxewOOp/hHrOo8HWLIEeOcd+EaMQODSS5Hx+efARx8BP/4xcMUV6mJWiqIe98zLWl/XmOPs2gV895268JaiAF27Al26qJejNfZrLY5xtq/37wf274diMMCgKECHDkD79jVrOJfGvrQ35v4HDgBFRaezaN8eyM9vXD16qHoekSyS/HkkdR4HDqCiqAg5gGb/v9kAiqPZG4AZG4CfdQH+eUVcHyoplZeXAwBycpJ0x9gzGzvhr2fMACZPrr3BcbbGSF2+f67v+Xx6/2SIiDRXAbAB1BiJbAAt2w9c+xHQqxmw9Ya4PlRSSsoGUCAA7N4NbNsGbN2q9p5s26Z3VbUzGAC7PfaHzVbta+W992AIhQCjEbj1VvWzwaB+hC+f7br63l7rYyxfDixdCpjNak7/7/8B1113+udw5s+lMV/H45jhr//zH2DxYihmMwyBADB+PHBDnF5A4rVM/ZtvAm+8cTqLm24CbrwxPo8VT0uWAG+8cTqLJH8eSZ3HkiWoeOMNTRtAus8Ce/HFF/HMM8+guLgY/fr1w5/+9CcMGTKk1tuXlZXhsccew9tvv40TJ06gQ4cOWLBgAUaPHp3AqutmYNVU+J1lgDsAOHT/acsSDAb1LqF2oZB6KmLr1tONnW3bgB071F6WurJaz9roiPv3zOa6/ZObMweGpUuhWK0w+Hzq6SO9TuE1xJw5auPnzN64AQOS73ksXgzX1KnwPPggcl98UX0evXolz/OYM0f9Z3tmFj17Js9zACLPo0YWSfo8kjqPcBaTJwPz52t3XE1GEjXQG2+8oVitVmXRokXKtm3blLvuuktp2rSpUlJSEvP2Xq9XGTx4sDJ69Gjl888/V/bu3ausXr1a2bRpU50fM5GDoEMhRWn5D3Ug9Jexn1JaEzEIOhRSlIMHFWXFCkV59llFmThRUS64QFEyM8MjTWp+OByKMniwokyYoChXXaVeZ7Gonx96SFFOnFAUl0tRgkF9n1tdJftgz9rqTeLnkbQD0pmFLKmQR1Sthw8f1vT/t659EvPnz8ddd92FiRMnAgAWLlyI5cuXY9GiRZgyZUqN2y9atAgnTpzA2rVrYbFYAAAFBQWJLLleDAZ1QcSPD6oLIg5ppXdFsoSnNGq9tkOtjh1Te3LO7NUpK4t9e6sV6N4d6N1bfQfeu7f6UVCgnnaZMwf4xz9qvrNq0iS53llVjWMq+9WvAKcTmeHap09XP0t/LsFg7EHn4a8l9zRGi3oezqNHAVT9bSTT82AWsqRCHlHPwbV7t6aH1m0MkM/nQ0ZGBv7zn/9g3LhxkesnTJiAsrIyvPvuuzXuM3r0aOTm5iIjIwPvvvsuWrZsiVtuuQWPPPIITLWsZ+D1euGNOmVRUVGB/Px8HDlyBEajEVlZWaisrERmZia8Xm/kOMFgEDabDU6nM3Kb6M9utxsWiwWhUAiKosBiscDtdiMzM7Pabed93wzzt1nwiy4+/GGAEwaDASaTCV6vFxkZGTWO63Q64XA44Pf7YTQaYTAY4Pf74XA4atw2um6z2QxFUSJ1u1yuGrWE67ZarQgGg2etOysrCy6XCzabDYFAoM51+3w+mEymSN12uz3mzzAzMxNlZWUwm82w2+0Nqtvj8cSsxX3kCBx79kDZuhXmnTth2rkTxu3bYSyNvSy3YjIh1KkTQj17ItSjB3zdusHUrx8qW7dGVtOmNer2eDzI/OMfYX/iCbimTkXo0UcjP8PQ7NnImjcPlY88AuP06ZGfYbhus9lcp+zDP2+fzxcze6fTiYyMjMjvrMFgQCAQqNPvrKIoCIVCsFgsMMyaBYvDgbL77oPRaITT6UTLli3hcrnQZMECKIEA3I88Uq+6jUZjnX5n6/u3Fl33uX5nw6dX4/G3pvVrRKy/NZ/PB5/Ph9zc3LR+jfB4PJHstXyNcLlcsNvtdfpbKy0thcPhgMlkanDdVqu1Tr+zEl8j4lF3Q18j9u3bh969eyf/GKDS0lIEg0Hk5eVVuz4vLw87d+6MeZ89e/Zg1apVuPXWW/HBBx/ghx9+wK9//Wv4/X7MmDEj5n3mzp2LWbNmaV5/XfVrFgIAbD6ZBAtOJZjT6Yw0gBp4ABh37IB940ZYdu9GztatsOzahYzDh2PeXDEYEOzQAejVC94uXWDu1w/Ojh1h69sXXqDGixvOsuiWIRiE59FH4fnd72CNut41eTKsVisMbnfDnlOCuR5+WH1nW1kJp9MJl8sV+Z7vkUfUhkR6zZMQwel0RhpApC+Xy4VQKBT3STN0bm6NX1d16wE6fPgw2rVrh7Vr12LYsGGR6x9++GGsWbMGX375ZY37dOvWDR6PB3v37o20DOfPn49nnnkGR44cifk4tfUAJWIWGAB8VwacvwSwm4BTEwFzuq+9HbWsefifbUZGhvq92pZm93iAnTurn7bauhXYu7f2x8nPr37aqlcvoEcPIFGn25JQjTxIN8xCDmYhR3FxMdq0aZP8PUAtWrSAyWRCSUlJtetLSkrQunXrmPdp06YNLBZLtdNdPXr0QHFxMXw+H6xWa4372Gw22Gw2bYuvhy45QJYFqPQDu8qAXun+hi68rDmAyl/9CkDVC0t4LMp996lTaKPH6nz/vTorK5a8vJpjdHr2BJJpar0Q4eX++UKvP2YhB7OQI2U2Q7VarRg0aBAKCwsjY4BCoRAKCwtx3333xbzP8OHD8frrryMUCsFoVLtSvvvuO7Rp0yZm40cCowHolwv8r0TdGDXtG0BRA2yblperDZUlS9TGjtEIvPCC+nGmZs2q9+aEP7dokdj6U1jSboaagpiFHMxCDq0nzOg6C2zy5MmYMGECBg8ejCFDhmDBggVwOp2RWWG333472rVrh7lz5wIA7rnnHrzwwgu4//778Zvf/Abff/89nnzySfz2t7/V82mc04AWVQ2gUuBnXfWuRoBp0wCXC9annqp+fSgEZGVVb+CEGz2tW8dv0TYCcPr8Ot/p6o9ZyMEs5PB4PJoeT9cG0Pjx43Hs2DFMnz4dxcXF6N+/P1asWBEZGF1UVBTp6QGA/Px8fPTRR3jggQfQt29ftGvXDvfffz8eeeQRvZ5CnQyo2hl+Y+xJSOnnxAlgxYrTX5tMwLvvqg2d9u3Z0NFJeGkJ0h+zkINZyGE2a9tk4VYYCfBNKTDwbaCpFTgxIc3/v5eVASNGABs2AAAUiwUGv1/fzUMJgLrKOgA0bdpU1zqIWUjCLOQoKipChw4dNPv/ne5zkhKiVzPAYgTKfMC+U3pXo6OKCmDUqEjjx3PnnSgrKVEbP9OnqwOhSTeKoiDN3g+JxSzkYBZyaJ0Dd6dKAKtJbQRtOq4OhO6YjstJVFYCY8YAX3yhfv3rXyMwbx4sQLWB0Yj+mhKKXf1yMAs5mIUcWmfBBlCCDGxR1QAqBa7vqHc1CeZyAWPHAp9/rm7cOXEi8OKLcB87BqBqlkUyLc2eosKDPTnrRX/MQg5mIUdKDYJOJ+GB0N8c17eOhPN4gHHjgNWr1T2yVq4Ehg4FEGNKI3t+dJWwPdnonJiFHMxCDq1n4rEBlCADqpar+SadZoJ5vcBPfqI2ejIzgQ8/jDR+AC4wJg3zkINZyMEs5EiZhRDTTb/mgAHAYRdw1A20cuhdUZz5fMCNNwIffAA4HMDy5cDw4dVuwi5lWZiHHMxCDmYhh9a9cZwFliBZFqBr1e4MKd8LFAgAt9wCvPceYLcDy5YBl15a42aVlZWRd1ekP+YhB7OQg1nIoXUPEBtACZQW44CCQeC224C33gKsVuCdd4Arr4x506ysLL67EoR5yMEs5GAWcrAHKIml/DigYFCd4fXGG4DZDPznP8DVV9d6c5fLFdlpmfTHPORgFnIwCznCM/K0wjFACRRpAKViD1AoBPzqV8A//6lubbF4sTr1/SxsNluCiqO6YB5yMAs5mIUcWm96zgZQAoVPgX1fDlT4gGyZG9jXn6IA990HvPKKuqP7v/8NXH/9Oe8WCAQSUBzVFfOQg1nIwSzk0DoLngJLoJYOoF3VKczNqdILpCjAAw8Af/mLusnZP/4BjB9fp7saDAYY0npjNFmYhxzMQg5mIYfWObABlGApNRBaUYCHHwaee079+pVXgJ/9rM53N5lMMJlMcSqO6ot5yMEs5GAWcmidAxtACZYyA6EVBXj8ceAPf1C//utf1QHQ9eD1euH1euNQHDUE85CDWcjBLOTw+XyaHq9RY4B8Ph/27t2Lzp07w2zmcKK6GJgqA6HnzAGefFK9/Kc/Ab/8Zb0PwZVVZWEecjALOZiFHA6HtisIN6gHyOVy4Y477kBGRgZ69eqFoqIiAMBvfvMbPPXUU5oWmGrCp8C2nQC8ybrv59y5wIwZ6uX589UB0A3ABcZkYR5yMAs5mIUcIhZCnDp1KjZv3ozVq1fDbrdHrh8xYgQWL16sWXGpqH0W0MwGBBRg20m9q2mA+fOBRx9VL8+dqw6AbiAuMCYL85CDWcjBLOQQsRDi0qVL8cILL+Diiy+uNiq7V69e2L17t2bFpSKDIWogdLKNA3rhBeB3v1Mvz5oFTJnSqMPxnZUszEMOZiEHs5BDxGaox44dQ6tWrWpc73Q6OV2wDga0AFYdTrIG0F//CvzmN+rlxx4Dpk1r9CH5rkoW5iEHs5CDWcghogdo8ODBWL58eeTrcKPn5ZdfxrBhw7SpLIUl3VT4RYuAu+9WLz/0kDoAWoOGrtPp1LxFTw3HPORgFnIwCzm03pKkQT1ATz75JEaNGoXt27cjEAjgueeew/bt27F27VqsWbNG0wJTUXgq/ObjQDAEmCQvRvCvfwF33qlevv9+YN48TRo/gPYj+qlxmIcczEIOZiFH9JhjLTToX+/FF1+MTZs2IRAIoE+fPvj444/RqlUrrFu3DoMGDdK0wFR0fg7gMAHOAPBDhd7VnMXixcCECeqaP/fcA/zxj5o1fgDA7/fD7/drdjxqHOYhB7OQg1nIoXUODV68p3PnznjppZe0rCVtmIxA3+bAl0fVcUDnN9W7ohjefhu49VZ1k9M771QHQGu9DLlRctdX+mEecjALOZiFHFpn0aCjmUwmHD16tMb1x48f55LhdSR6HNCyZcBNNwHBIHD77eoA6Di8CHCPHVmYhxzMQg5mIYfWOTSoB0hRlJjXe71ezberT1XhcUAbpc0EW7EC+OlPAb8fuPlmdQB0nN4BsVtZFuYhB7OQg1nIofVu8PVqAD3//PMA1FbYyy+/XG16YDAYxGeffYbu3btrWmCqil4LSFE0P7vUMJ98AowbB/h8wE9+Arz2GhDHHj0OLpSFecjBLORgFnJoPQi6Xg2gP/7xjwDUHqCFCxdWO91ltVpRUFCAhQsXalpgquqTC5gMwHEvcNAJ5Ou91MSaNcC11wJeL3DddcD//R8Q5/3dwouLca8dGZiHHMxCDmYhh64LIe7duxcAcPnll+Ptt99Gs2bNNC0mndjNQM9mwJYTai+Qrg2g//0PGDMGcLuB0aPV2V8WS9wflguMycI85GAWcjALOUQshPjpp5+y8aMBEQOhv/wSGDUKcDqBH/8YeOstwGZLyENziXlZmIcczEIOZiGHiK0wAODgwYN47733UFRUBJ/PV+178+fPb3Rh6WBAC+C173XcEmPDBmDkSODUKeDyy4GlSwGNz7GeDd9ZycI85GAWcjALObTuAWpQA6iwsBDXXnstOnXqhJ07d6J3797Yt28fFEXBwIEDNS0wlenaA7R5M3DVVUB5OXDJJerU9wSf4+a5dVmYhxzMQg5mIYfWPUANOgU2depUPPjgg9iyZQvsdjveeustHDhwAJdeeiluuOEGTQtMZf2rpsIXVQLHPQl84G3bgBEjgBMngAsvBJYvBzRuWddFZmam5i16ajjmIQezkINZyKF1I7RBDaAdO3bg9ttvBwCYzWa43W5kZWVh9uzZmDdvnqYFprIcK9CpiXp5U6J6gXbuBK68EigtBQYPBj78EGjSJEEPXp3X64XX69Xlsakm5iEHs5CDWcihdQ4NagBlZmZGxv20adMGu3fvjnyvtFTayn6yhRdETMg4oO+/B664AigpAfr3Bz76CGjaNAEPHJvZbIY5zlPtqe6YhxzMQg5mIYfWOTToaBdeeCE+//xz9OjRA6NHj8bvfvc7bNmyBW+//TYuvPBCTQtMdQOaA2/tTcA4oL171cbPkSNA797AypVAbm6cH/TsaltRnPTBPORgFnIwCzm0zqJBDaD58+dHBobNmjULlZWVWLx4Mbp27coZYPWUkB6goiJ1ltfBg0CPHkBhIdCiRRwfsG6CwaDeJVAU5iEHs5CDWcihdRYNagB16tQpcjkzM5OrPzdCuAG0qxxw+oFMrdcfPHRI7fnZvx/o2lVt/LRqpfGDNIwtQesNUd0wDzmYhRzMQg6ts2jQGKBOnTrh+PGa52zKysqqNY7o3NpkAHkOIKQA357Q+ODFxWrjZ/duoFMnYNUqoE0bjR+k4VwuF1wul95lUBXmIQezkINZyOF2uzU9XoMaQPv27YvZFeX1enHo0KFGF5Vu4nIa7OhRdbbXd98B7durjZ/zztPwARqP00tlYR5yMAs5mIUcWk+Dr9cpsPfeey9y+aOPPkJOTk7k62AwiMLCQhQUFGhWXLoY2BxYcUDDgdDHj6vr/GzfDrRrB3z6KdChg0YH1w4XGJOFecjBLORgFnLouhXGuHHjAAAGgwETJkyo9j2LxYKCggI8++yzmhWXLjTtATp5Ut3Ta8sW9XTXp5+qp78E4hLzsjAPOZiFHMxCDl23wgiFQgCAjh074quvvkILATOJUkG4AbTlBOAPAZYGnZiEuq3FyJHAN9+oA50LC9WBz0LxnZUszEMOZiEHs5BD160w1q1bh/fffx979+6NNH5ee+01dOzYEa1atcIvf/lLrpjZAB2bANkWwBcCdpxs4EFOnQJGjwa++gpo3lxt/PTooWmdWsvKyuK7K0GYhxzMQg5mIYfWPUD1agDNmjUL27Zti3y9ZcsW3HHHHRgxYgSmTJmCZcuWYe7cuZoWmA6MhtP7gjVoHJDTCVxzDbB2LdCsGfDJJ+pih8K53W7NR/VTwzEPOZiFHMxCDo9H200z69UA2rx5M6688srI12+88QaGDh2Kl156CZMnT8bzzz+PJUuWaFpguojsDH+2cUAzZwJz5lS/zu0Grr0W+OwzwGZTV3ju3z9OVWrLarXCarXqXQZVYR5yMAs5mIUcFou2C+XVawzQyZMnkZeXF/l6zZo1GDVqVOTrCy64AAcOHNCuujQyoC49QCYTMH26ennaNMDjAcaNU6e4A8CECcCgQfEsU1NcYVUW5iEHs5CDWcih60rQeXl52Lt3L/Lz8+Hz+bBx40bMmjUr8v1Tp05p3kJLF+EeoE2l6qKIRkOMG02bpn6ePh0IBoGvvwY+/li97o47gL/+NSG1aoV77MjCPORgFnIwCzl03Qts9OjRmDJlCubNm4elS5ciIyMDl1xySeT73377LTp37qxpgemiRzPAZgIq/MDeU0Dn7FpuOG0aoCjAjBmnr5s4EXj55YTUqSU2lmVhHnIwCzmYhRxaZ1GvMUBz5syB2WzGpZdeipdeegkvvfRStXOjixYtwlVXXaVpgenCYgR6N1Mvn3M9oMsui7qjBVi0KF5lxRUHF8rCPORgFnIwCzm0HgRdrx6gFi1a4LPPPkN5eTmysrJgMpmqff/NN9/kdMFGGNAC2FAKbCwFfnq2tQsffVT9bDQCfr86MDp8eiyJcHl5WZiHHMxCDmYhh65bYYRFb4ERLTc3t1HFpLvITLCzDYSeMwf43//Uy//3f8CuXdUHRicRLjAmC/OQg1nIwSzk0HUrDIqvc26JMWfO6caO2ayu+nzjjerXSdgIYm+hLMxDDmYhB7OQQ9etMCi++uaqs79K3MARF9DmzDccwSAwahTw4YfAj34EhHviwo2eJJuuyXdWsjAPOZiFHMxCDvYApbBMC3B+DrCjTO0FatP+jBvMnKnu8g6oKz9HS6KenzC+s5KFecjBLORgFnLouhUGxd9ZT4NVVABr1qiXz2wAJSGXywWXy6V3GVSFecjBLORgFnJoPRuPDSBhzjoQ+uOPgUAAOP980bu815XNZoPNZtO7DKrCPORgFnIwCzm03pKEp8CEOWsP0LJl6ucU6P0BgEAgoHcJFIV5yMEs5GAWcmidBXuAhAn3AO05BZT7or4RDAIffKBeTpEGkMFggMEQa88P0gPzkINZyMEs5NA6BzaAhMm1A+2rxtxtiu4FWr8eKC0FmjYFhg/XozTNmUymGotpkn6YhxzMQg5mIYfWObABJFDMcUDh019XX61uf5ECvF4vvF6v3mVQFeYhB7OQg1nI4fP5zn2jeuAYIIEGtADe3X/GOKD331c/p8jpL4DrakjDPORgFnIwCzkcDoemx2MDSKAaPUD79wNbtqh7f40apVtdWuMCY7IwDzmYhRzMQg4uhJgGwjPBtp8E3AHAEe79GT4cSKH91rjAmCzMQw5mIQezkCMlF0J88cUXUVBQALvdjqFDh2L9+vV1ut8bb7wBg8GAcePGxbfABDsvE2huA4IKsPUEUvL0F6C+swq/uyL9MQ85mIUczEIOrXuAdG8ALV68GJMnT8aMGTOwceNG9OvXDyNHjsTRo0fPer99+/bhwQcfxCWXXJKgShPHYIhaD+iwB1i1Sv1i7Fj9ioqDrKwsvrsShHnIwSzkYBZypFwP0Pz583HXXXdh4sSJ6NmzJxYuXIiMjAwsWrSo1vsEg0HceuutmDVrFjp16pTAahNnYLgBtOUI4PMBnToB3bvrW5TGnE6n5i16ajjmIQezkINZyKH1liS6jgHy+XzYsGEDpk6dGrnOaDRixIgRWLduXa33mz17Nlq1aoU77rgD//3vf8/6GGdOYayoqACg/iA9Hg+ysrJQWVmJzMxMeL3eyDoDwWAQNpsNTqczcpvoz263GxaLBaFQCIqiwGKxwO12IzMzs8ZtXS4XbDYbAoEADAYDTCYTvF4vMjIyatzW6XTC4XCgqx0AsrCxRN3h3T9yJE4eO1ajlnDdZrMZiqJE6na5XDFrcbvdsFqtCAaDcanb5/PBZDLBYDDA7/fDbrfH/BlmZmbC4/HAbDajvLy8QXV7PJ6YtbhcLtjtdvj9/kjdPp8PDocjZt0ZGRmR7Otat8Viify8rVbrOX+G4brNZvM5f4YNrTsQCNTpd1ZRFIRCoRrZh/8uMjMzG1W30WiE3++PWXdj/tZqq7u2nzeAOv3O+v1+GI3GSPZa192Q14hgMAifzweXy6VZ3cn6GhH9t6bHa4TL5YLD4cCJEyfS/jVCq7ob8xqhJV17gEpLSxEMBpGXl1ft+ry8PBQXF8e8z+eff45XXnkFL730Up0eY+7cucjJyYl85OfnN7ruROjbTH0B32Jvi6DBiODo0TpXpD2/3w+/3693GVSFecjh8/mYhRB+v1/z9WeoYbTeCsOgKIqi6RHr4fDhw2jXrh3Wrl2LYcOGRa5/+OGHsWbNGnz55ZfVbn/q1Cn07dsXf/7znzGqajr4z3/+c5SVlWHp0qUxHyNWD1B+fj7Ky8uRnZ2t/ZPSSEgBsl8JwhkyYdszF6Dntv8BGm8Ep7fy8nIAQE5Ojs6VEMA8JGEWcjALOQ4cOID27dtr9v9b11NgLVq0gMlkQklJSbXrS0pK0Lp16xq33717N/bt24exUYOBQ6EQAMBsNmPXrl3o3Llztfsk606+RgPQz30Ia23t8c3VP0PPFGv8ANrv60KNwzzkYBZyMAs5UmovMKvVikGDBqGwsDByXSgUQmFhYbUeobDu3btjy5Yt2LRpU+Tj2muvxeWXX45NmzYlzemtuhrwvToO6pv+I3SuJD54ykUW5iEHs5CDWcih9Skw3RdCnDx5MiZMmIDBgwdjyJAhWLBgAZxOJyZOnAgAuP3229GuXTvMnTsXdrsdvXv3rnb/pk2bAkCN65PeoUMYsPFjoPd4fNOsq97VxIXdbte7BIrCPORgFnIwCzm0PpujewNo/PjxOHbsGKZPn47i4mL0798fK1asiAyMLioqgtGo+2z9xFu+HAOKvgEAfHPKCkVR1wdKJeER/Vqv7UANwzzkYBZyMAs5tJ4Gr+sgaD1UVFQgJydH/CBoXHstvB9+hKwXXAgYTNh3M9Chid5FaSv8y8w9dmRgHnIwCzmYhRzFxcVo06aNZv+/07BrJQm43cAnn8AW8KFXpjr9MrIxagrhEvOyMA85mIUczEKOlFoHiGqxapXaCGrfHgPOU88/byzVuaY44BLzsjAPOZiFHMxCjpTbCoNiiNr8dEALdeDPNynYAOI7K1mYhxzMQg5mIYfWPUC6D4KmMyhKtQZQZE+wFDwFxkGFsjAPOZiFHMxCDq3HYbEHSJrNm4GDB4GMDODyy9EvFzAAOOQEjrn1Lk5bHo8HHo9H7zKoCvOQg1nIwSzkiN7VQQtsAEkT7v358Y8Bux1NrECXqhXYU60XyGKxwGKx6F0GVWEecjALOZiFHGaztiet2ACSZtky9fM110SuGtBc/Zxq44AURUGarcIgGvOQg1nIwSzk0DoHNoAkKSkB1q9XL48ZE7l6QHgcUIo1gILBIILBoN5lUBXmIQezkINZyKF1DhwELckHH6ifBw8G2rSJXB3pAUqxU2DJuEltKmMecjALOZiFHFpnwR4gSWKc/gJO9wB9Xw5UptCefC6XS/OlzanhmIcczEIOZiGH263tTCD2AEnh9QIff6xeHju22rdaOYC2GcBhF7D5ODC8tQ71xQGnl8rCPORgFnIwCzk4DT5VrV4NOJ1A27bAgAE1vp2K44C4wJgszEMOZiEHs5CDCyGmqvD09zFjYm77PqA5sLwotcYBcXl5WZiHHMxCDmYhh9a9cWwASRC9+vMZp7/Cwj1AqbQnWPhdFXdZloF5yMEs5GAWcrAHKBVt2wbs2wfY7cCVV8a8SXgm2LaTgC8IWE2JKy9e+M5KFuYhB7OQg1nIwc1QU1G49+eKK9QtMGIoaAI0tQL+kNoISgVut1vzUf3UcMxDDmYhB7OQQ+stSdgAkuAcp78AdVhQqg2EtlqtsFqtepdBVZiHHMxCDmYhh9ZbkrABpLfSUmDdOvVy1OrPsaTagohcYVUW5iEHs5CDWcjBlaBTzYcfAqEQ0K8fkJ9/1pumWg8Q99eRhXnIwSzkYBZyaJ0FG0B6q8Ppr7BwD9DmE0BIAYw1Z8snFe6wLAvzkINZyMEs5OApsFTi8wErVqiXz9j+IpbzmwJ2k7odxg/l8S0tETwej+aD2qjhmIcczEIOZiGH1+vV9HhsAOnp88+BigqgVSvgggvOeXOzEeibq15OhXFAGRkZXFtDEOYhB7OQg1nI4XA4ND0eG0B6il792Vi3KFJpHBCXmJeFecjBLORgFnJwIcRUoSi17v5+Nqk0E4wLjMnCPORgFnIwCzm4FUaq+O474IcfAKsV+PGP63y36B4gRYm5bVjS4BLzsjAPOZiFHMxCDvYApYrw6a/LLgOaNKnz3frkAiYDcMwDHHYB7bRtECcU31nJwjzkYBZyMAs52AOUKhpw+mvm14DJCHRvqm6HsbH0dANozkYgGAJmDta+1HhxuVwA+M5KCuYhB7OQg1nIofWWJBwErYeTJ9UZYEC9GkAmIzD9a7UHCDg9EHrOxqrrkyxNu90Ou92udxlUhXnIwSzkYBZy2Gw2TY/HHiA9fPQREAwCvXoBHTvW+W7TBqqfp3+tfv76GDB7AzBjAzB78OnvJwu/3693CRSFecjBLORgFnJonQUbQHpowOmvsGkDgb0VwN+/A5YVqR/nZQL7TwHzvwV6NVM/2mXKHyBtkF5gmmEecjALOZiFHFpnwQZQogUC6v5fQJ22v4jlL5cAr34HhHdFOegEXtlV/TY5VqBns9MNovBHmww5DSOTyaR3CRSFecjBLORgFnJonQUbQIm2bp06Big3F7jwwgYd4unNauPHagR8IeCGTlUDo0+og6N/qADKfcC6EvUjWlNrVIMoF+jZVP3c2pH4hpHP50vsA9JZMQ85mIUczEIOngJLduHTX6NHAw1ozYYHPIfH/ER//dZV6m28QWBXGbD9pNogCn/8UAGU+YD/lagf0ZrZavYW9WoGtIpjw0jrZc2pcZiHHMxCDmYhh9aD0dkASrR67P5+pjMbP0DNgdHTBgI2E9C3ufoRzRMAdpVXNYhOnG4Y7a4ATnqBz4vVj2jNbWoP0ZkNo5YavCZwgTFZmIcczEIOZiEHF0JMZrt3Azt2AGYzcNVV9b57MBR7tlf462Do7Pe3m4F+zdWPaO4AsLPsdIMo3HO0pwI47gU+O6J+RGtpjzHGKBdocY4Gengto2kDay4wloxrGaUSLvgmB7OQg1nIwYUQk1m49+eSS4CmTet997M1DBozBd5hVrfYCG+zEeYKN4xOVD+VtveUuhL1miPqR7RWjtin0nKrGkbhtYwA4FfnnX5nFd27RfrgO105mIUczEIO9gAls0ac/tJDhhkY2EL9iOb0AzvKqp9K214G7DsFHHWrH58ern6f1o7Tp9LGtlcbOxXuppg1IBDz1B4lHt/pysEs5GAWcmjdA2RQFEU5981SR0VFBXJyclBeXo7s7OxEPjDQogXg96sboXbtmrjHTpBKP7DjjIHX204CRZVnu5cCwIB2GUD3ZkATi/qRbQGaWE9/HfmIui476rI5watgR5/KO1MyncqLfh7Hjh0DALRs2RJA8jwPZiEHs5AlFfKIfg579uxB586dNfv/zR6gRPn4Y7Xx061bSjZ+ACDLAlzQSv2Idsqn9hCdeSrtoBMA1Clmh1zqR0PZTbEbSWc2lOpymwzzuWe+RZ/Ki35xSbZTedHPY/L5p7v4k+l5MAs5mIUsqZBH9HO4s422M/LYAEqUJDv9paUmVmBoK/UjLPwHaDEo8CsG3NIZGN0eOOUHKnzq5xofUdeHb+OrGvjtCaofxzyNr9doALLMsXugohtKV7ZVn8PGUmB8J+CdfcCSPcBNnYG+ucCy/eqxTAb1s7Hq2NWui/qeyVj9NjVuh1ruW4fHMCB2oy56FqHbZcCDPT2YvyszqU5JxpoJmYynVZmFHKmQBZAaeUQ/h7IO2q7JwlNgiRAMAq1bA6WlwKefApddlpjHFSr8B/hobw8e7uXF87tzGvwH6QvGbiRVnNFgivn9M25T6T+9unYqMqD2xpO3qgEZPiWZYQYyq94eRTecDKh5Odb3G3Kf6Osbcp8THnXWoqHqWTS3nXtW4pnHqI/63qWuj3HMrTbkDVCgwICWdnVyQTI5GnkOahbJ+ByA6OeRvFkAqZHHUTdw7GQFMEm7/9/sAUqE9evVxk9ODjB8uN7V6Cr63cf9XXwADDHfpdSV1QQ0NwHNNVgfK6SoM9/CDaNYjaTohlT4+//ZE242AMNbq8cJfwTDlxHjujO+V+P6qu8FQ9XvH33b+jTYFAABBee4k/pf2hVQP5JR+Okd96ofyUqpyuKYR5ueTT2Es0jm5wCkRhZA6uShFTaAEiF8+mvUKMBi0bcWnUWvZXT8+Ollzeu6llE8GQ3qOKYsi7pnWl3M2Qi8uef0tiRXnZfYbmWlqhEUs3FV2/UxGlYvbAWe33b6lOR9PYG7e1ZvKylnPG6drqvjfaKvb+h9Xt2l7olnMQL+EHDH+cCEbjinhvT61bffvD43f+07dbNjs0FBQDFgYjfgtjo8D0n+WfUcwlkk43MATj+PcBY/7wbcloRDOP/5vbp/ZDiPZHwe//weeHWzxgdV0kx5ebkCQCkvL0/cg/bpoyiAovzrX4l7zCRQWVmpVFZW6l1Gg83eoCj4q/o51tfJIlz34+u8SmVlZVI+D2YhB7OQJRXyCNf80CfHNP3/zR6geNu/H9iyBTAagauvbtShZr69GSajAdPG9a3xvTlLv0UwpGDm9f0a9RiJFF7USuu1HRKhrtuSSBf9PH51XhmcTmDaQDWPZHkezEIOZiFLKuQR/RxuySnHMxoemw2geFu+XP08fDjQvPnZb3sOJqMB099S+wCjG0Fzln6L6W9txuyfJE/jB0juBcYauy2JFNHPw+U6nUcyPQ9mIQezkCUV8oh+DsXFXAixURI+C2zUKGDFCmDePODhhxt9uOjGzrRxfWt8nUyOHj0KAGjVqtU5bkmJwDzkYBZyMAs5du/ejS5dunAWWFKorARWrVIvX3ONJoecNq4vQiEF09/ajFnvqKe9krHxAyR3D1AqYh5yMAs5mIUc3Aw1mRQWAj4f0KkT0KOHZodt3VRdwCEYUmA0AA+N7qXZsROJmwzKwjzkYBZyMAs5tN4MNcE7KKWZZcvUz9dc07CV1mJwevx48PUNka9DCtDtoaU4VpF8izpkZmYm5QDoVMU85GAWcjALObRuhLIBFC+h0OkB0Bqd/gKA6xasRqU3gKYZVqx46ErYLSYcOOHC+Q+/i52HyzV7nETweDzweJKv4ZaqmIcczEIOZiGH16vtyqZsAMXLxo1AcTGQlQVceqkmh5y6eCMKtxUDAF64/QKM7NsW3/x+DJplWnHS6cOAx5dj1bYjmjxWIlgsFljSfGFISZiHHMxCDmYhh9ms7agdNoDiJXz6a+RIwGrV5JCrd5YAAPq1b4abh3UEAHRvm4NdT1+H/NwMePxBjHymEH//7AdNHi/eFEVBmk1CFI15yMEs5GAWcmidAxtA8RLe/kKj01/7Syuxcd8JAMBT4wfAaDw9pqhlth3fPTMO44d2QCCo4BcvrcNjb36DUEj2H20wGEQwGNS7DKrCPORgFnIwCzm0zoENoHg4dEg9BWYwAKNHa3LIGW9thi8QwmU98jCyT9sa37dbTXj915fgsWt7AwCefG8rbvnzf+H2yd3R0mq1wqpR7xg1HvOQg1nIwSzk0DoHNoDiITz4eehQQIPFs7YeOInX/rcHADBv/EAYaplRZjQa8PsbBuDvd10Ei8mIxV/ux5VzPxE7Q8ztdsPtdutdBlVhHnIwCzmYhRxaD0ZnAygeND799eibm6AowE8uaI8hnVuc8/Y//1FnfPzIlWiaYcW6H45h6MwPseOQvBlinF4qC/OQg1nIwSzk4DR46dxu4JNP1Mtjxzb6cJ/vOopl3xyEyWjAEzf0r/P9LuvRGutmXI1OrbKw91glLpq9QtwMscrKysgiY6Q/5iEHs5CDWcjBhRClW7VKbQTl5wN9+jTqUIqi4JHFGwEAd1zaBee3yanX/bu3zcEXM0bhoq4tUebyiZshlpWVxWXmBWEecjALOZiFHFr3xLEBpLXo01+NXP35vY0Hsfb7Y3BYTZjx/xq211fLbDsKp/wYN11YIG6GGN9ZycI85GAWcjALObTuAeJeYFpSlNMNoEae/goEQ3j0zW8AAJNG9kDbZg0/92m3mvDvey5Gl7wm+P27W/Dke1uxu+QU/v7Li+Cw6vcrwHdVsjAPOZiFHMxCDvYASbZ5M3DwIJCRAVx+eaMO9drne7D9UDmaZVrx8JjGb3ZqNBow56f98eov5cwQc7lccLlcuj0+Vcc85GAWcjALObSejccGkJbCvT8jRgB2e4MP4/YFMOPtzQCAx67tg6aZ2q19MOESOTPEbDYbbDabLo9NNTEPOZiFHMxCjpRcB+jFF19EQUEB7HY7hg4divXr19d625deegmXXHIJmjVrhmbNmmHEiBFnvX1CaXT668WVu3DwhAv5zTNw74jzNSisust6tMYXM0/PEBs2+0NdZohxhVVZmIcczEIOZiFHyq0EvXjxYkyePBkzZszAxo0b0a9fP4wcORJHjx6NefvVq1fj5ptvxqeffop169YhPz8fV111FQ4dOpTgys9QUgKEG2KNWP25zOnDk8u2AgBmX98fdqtJi+pqOL/N6Rli5S6/LjPEuMeOLMxDDmYhB7OQI+X2Aps/fz7uuusuTJw4ET179sTChQuRkZGBRYsWxbz9v//9b/z6179G//790b17d7z88ssIhUIoLCxMcOVn+OADdRD0oEFA25pbVdTVvPe34qTTh17tcnDbxR01LLCmWDPEHl2SuBliZrNZ8919qeGYhxzMQg5mIYfWOeiaqs/nw4YNGzB16tTIdUajESNGjMC6devqdAyXywW/34/c3NyY3/d6vfB6vZGvKyoqIvfzeDzIyspCZWUlMjMz4fV6YTKpPS7BYBA2mw1OpzNym+jPbrcbFosFoVAIiqKgydKlMAPwXX01yo4erXZbl8sFm82GQCAAg8EAk8kEr9eLjIyMaset8JuwYMUOAMBjo7uh8tQpGAwG+P1+OByOGjVE1202m6EoSqRul8uFzMzMmHVbrVYEg0EoigKLxYIFPz0fHXLtmPfBTsxdthXbikqx6M4LoQS8dao7KysLTqcTDocDPp8PJpMpUrfdbo/5M8zMzERJSQnMZjNCoVCD6vZ4PDFrcblcsNvt8Pv9kbp9Pl/Mn6HT6URGRkYk+7rU7fF4YLFYIj9vq9UKt9sds+5w9uG6zWbzOX+GDa07EAjU6XdWURSEQiFYLJZqdXu9XrhcLuTn5zeqbqPRWKff2fr+rdVWd20/bwB1+p31+/0wGo11/ltr6GtEXeoO/62Vl5dH/pa0qrsxrxF1rVvr14gz/9b0eI04cuRI5Lbp/hqhVd0NfY0oLi6ua/OiTnTtASotLUUwGEReXl616/Py8ur8RB955BG0bdsWI0aMiPn9uXPnIicnJ/KRn5/f6Lpr8HphWrUKABAcNarBh3ny/e3wBEK4sHMuRvZu/B5idWU0GjD9ul54/qbesJgMeG9zMUbP/wzHTnnPfedGcDgccDgccX0MqjuHwwF7Iwbvk3b4tyGH3W5nFkJo/fpkUHQ8uXn48GG0a9cOa9euxbBhwyLXP/zww1izZg2+/PLLs97/qaeewtNPP43Vq1ejb9/YCwXG6gHKz89HeXk5srOztXkiH38MjBypnvo6eLBBCyDuPFyO3lOXIRhS8Pm0kRjeLXENoGirdxTj+ufW4KTTh44ts7D8d1egR7v6rUBdV+FxXq002DCWGo95yMEs5GAWcuzevRtdunTR7P+3rj1ALVq0gMlkQklJSbXrS0pK0Lp167Pe9w9/+AOeeuopfPzxx7U2fgB1CmN2dna1D82FZ3+NGdPg1Z8fe3MTgiEF1w48T7fGD1BzD7F4zhDjEvOyMA85mIUczEKOlFoI0Wq1YtCgQdUGMIcHNEf3CJ3p6aefxpw5c7BixQoMHjw4EaXWTlGAZcvUyw3c/f2LH47h7a+LYDQY8OQNAzQsrmFizRBbtEb7GWJcYl4W5iEHs5CDWciRcpuhTp48GS+99BL+8Y9/YMeOHbjnnnvgdDoxceJEAMDtt99ebZD0vHnzMG3aNCxatAgFBQUoLi5GcXGxfr+g27cD+/apCx/WMg7pbBRFwZTF6pYXEy7phF7nNdW2vgYKzxC7eZg6Q+yOl7WfIcZ3VrIwDzmYhRzMQg6te4B0n9s3fvx4HDt2DNOnT0dxcTH69++PFStWRAZGFxUVwWg83U77y1/+Ap/Ph5/+9KfVjjNjxgzMnDkzkaWrwr0/V1yhboFRTyu+PYw1O0tgsxgx6/p+GhfXONF7iM1ZugVzl23F7qOn8KpGe4iFW/MZDfi5kfaYhxzMQg5mIYfWW5Lo3gACgPvuuw/33XdfzO+tXr262tf79u2Lf0H1Eb37ez2FQqd7f+4b0R35zbVt3WrBYDBg9k/6o0teE9z58hdY8uV+FB134t1Jl6FVTuNmRnBmhSzMQw5mIQezkEPrWWC6nwJLaqWlQHi9ogY0gF5ftxffHjiJnAwLpo7trXFx2rr9YnUPsWaZVnzxQykunLWi0XuI+f1++P1+jSqkxmIecjALOZiFHFrnwAZQY3z4IRAKAf36AfVcX8jrD2LafzYBAB4Z0wvNm8jfbC88Q6xzqyaRGWKFjZghZjAYYGjgrDnSHvOQg1nIwSzk0DoHNoAaoxGnvxau+g77Sp1o09SB+0f20Liw+Dm/TQ6+mHk1hndTZ4hd3YgZYiaTKbLSJ+mPecjBLORgFnJonQMbQA3l9wMrVqiX67n7e4Xbh9+/uwUAMPP/9UWGTcRQrDpr0cSOTx5p/Awxn88Hn88XpyqpvpiHHMxCDmYhB0+BSfHf/wIVFUDLlsAFF9Trrn/4YDtKT3nRrXU2fnFplzgVGF/hGWLTxvUBAMxdthU3vfhfuH2BOh+Dy/3LwjzkYBZyMAs5OAhaiujVn411/zGWlLsx/0N1w9Mnb+wPsyl5IwjPEPvHry6CxWTEm+v344q5K3G03F2n+3OBMVmYhxzMQg5mIUfKLYSYtMINoHqe/pqzdAuc3gCGdGqO6we3j0NhiXf7xZ2x8pER9Z4hxgXGZGEecjALOZiFHCm1FUbS2rUL+P57wGIBfvzjOt/th5IK/PXT7wAA824amFIzCy7tkVfvGWJ8ZyUL85CDWcjBLORgD5AE4d6fyy4DmjSp892m/WczAkEFV/dti8t6nH2z12QUa4bYK6u/r/X2fGclC/OQg1nIwSzkYA+QBA04/bVh73G88cU+GAzAUzfqv+FpvIRniN1SNUPszle+wNTFG2POEHM6nZq36KnhmIcczEIOZiGH1lthsAFUXydPqjPAAHUAdB1NXaJueXHLsI7o1yE3HpWJYbea8K97Lsb0cX0BAE+9vy3mDLGMjAzuryMI85CDWcjBLOTQejYeG0D19dFHQDAI9OwJdOpUp7t8svUIVm49AovJiDk/kbXhabwYDAbM+km/s84Q83q98Hq9OlZJ0ZiHHMxCDmYhh9Y5sAFUX/U8/RUKKZiyZCMA4J4ru6Fjq7qPGUoFZ84QGzrzQ2w/VAaAK6xKwzzkYBZyMAs5uBK0ngIB4IMP1Mt13P7iP1/tx4a9J5BlN+Oxa2VveBov0TPE9pU6MXDachRuO1Jjj505S7/FzLc361hpeuOeR3IwCzmYhRzcC0xP69apY4Byc4ELLzznzf2BEB57cxMA4KHRvdAqJ31XEw3PEGvfPBNefwhXzfsEr/53DwIBdVzQnKXfYvpbm2Ey8oVGL4FAIJIH6YtZyMEs5NA6h+TahEpv4dNfo0cD5nP/6F5e/T1+KDmFVtl2TB6VPBuexkuLJnZ898x1uGDGB9hyoAz3v7EF+096YTSZ8YcPtmP2T/phWtXAaUo8m82mdwlUhVnIwSzk0DoLNoDqY9ky9XMdTn9VevyYtfRbAMD0cX2RZbfEs7KkYbOYsPmJa3DFkyuxemcJ5n+kLgxpNBjw9892Y9X2YrRvnokOLTLVz80z0b7qssPKX9d4Ck/11XqtDao/ZiEHs5BD62nw/I9SV7t3Azt2qD0/I0ee8+YLVuxASbkHnVpl4a7Lk3PD03gxGAz49LGrYJnwLwSq1gcKKQr2HqvE3mO1r7jasokNHVpknW4cnfG5eZaN5+obgYu9ycEs5GAWcmjdCGUDqK6WL1c/X3IJ0LTpWW9aesqDp5dvBwD8/qf9YTVzBsGZ5iz9FoGQAqvJAF9Qwe9G9cC4Qe1RdNyJ/aWVKDruqvrsxP7jTlR6Ajh2yotjp7z4eu/xmMfMsJrQvkUmOjTPQvvmGejQIqtaA6ldswxYzBz2Vpvwcv9c80R/zEIOZiGH1gtSsgFUV/U4/fXEu1twyuPHgA65GD+0IL51JaHwgOdp1/bElDE98OzHP2D6W5uRk2GNOQZIURScdPqqGkfOMz6rjaXicjdcviB2Hq7AzsMVMR/XaDCgbTNHtdNrZzaSmjjqdqpy5tvqgO1Y9c5Z+i2CIQUzr0+uNZ/4TlcOZiEHs5CDPUB6qKgA1qxRL5+jAbTvWCX+XKiOa3lq/AAYOaupmnDjZ/ZP+uFXF7VGZWVlpBEx/S11CvyZjQqDwYDcLBtys2zoX8sq2h5fEAdPxmogqZ+LjjvhC4Rw8IQLB0+48D8ci3mcZpnWmGOQwp/zsh0wGg0wGQ0x641+fskguiF35jvdZGnIpUpjlFnIkQpZAKmRR/RzYA+QHlauBPx+oFs39eMspr+1Gb5ACFf2ao0f926ToAKTRzCkRGZ7RQ9oC/+BBmPsGVYXdqsJXfKy0SUvO+b3QyEFRys81U6v7T9evZF00umLfGwuOhnzOFazEfm5agNpQIdmmP7WZmzcdwJ3XNoFb67fj9c+34M7L+2Cq/u2xeb9J2AxG2E1G2E1mWAxG2A1mWA1G2Exqdfr3UCObsj97qrTY9WSqSGXKo1RZiFHKmQBpEYe0c/hrgtbaXpsNoDqoo6nv74tOol/rd0DAHjqxoEckBtD9LsNt1vdFiP8ziqeU+CNRgNaN3WgdVMHhtYyJv2U2x/j9Joz0lA6dMINXyCE3UdPYffRU5H7Ld1wAEs3HIh8/fKaH/Dymh/qVJfJaIg0hqIbRtUum4xqQ8pkhNVsgsVkgNVsqv32Ne4T/b3q9x/SqQUmXtIZ09/ajB8On8Btw/Lx1qZjWLjqe9xzRTeMHXAeNu8/UbUYHGAAoi5Xfa7tcoJu+/CYXgiGQpj+1maEQgoeH9cHT7y7BTPe/hazru+Lx67tg1BIQW1/jlL+TqN7Ql0uFx4c2TVyejhZloiI1Zsb/c82GZ4DkBpZAKmRR/RzOFnaVtNjGxRFadhb7iRVUVGBnJwclJeXIzs7dm9BNcEg0KYNcOwYsGoVcPnltd50zB9W4YPNh3DDkA5Y8psfaVh1aqqoUMfq1CkHAfyBEA6XuWqcXntp9fdQFPUfc/e2OfAHQ/AF1I/I5WAQvkAI6fXXlnpitZUMiN2Ainnb2hphUccIhhSEon5RTFWnXJNJMKRU6801GQ0wm5LrOQBAIFj9eZiNBphNyTeRIhAMRWbcAsn5PALBEAIeF7DkV3X//30O7AE6l6++Uhs/OTnAxRfXerPPdpbgg82HYDIa8MQN/RNXXxJLtra3xWysmoZ/elDknKXfQlHUU2O+QAg3Dys467uqYOiMhtEZl6t/HYQ/qMAXCMIXDMEfCMFX9b1ql2s91lnuH+M+P5Sc7tVq28wBRYH6AaXqsgIFZ15X2+Vz3xY4/XWyiFWr+kxj3bheR671O2c2JpJRKjwHAAiEFARCQb3LaLRUeR6NxQbQuYRPf119NWCJPUNIURQ8sljd8PSuy7qia+vk6NHQWygU0ruERjmzKzn8NVD76TyT0QiH1Qhpm6KEa7eajPAFQ7j7im4J7x5XFKVRjaunl2/F3GXbIo3RKdf0woOje6nHrqWBEbNBU0uLLNa1tTXeYj1erbc94/oFH+3AHz7YDovJAH9Qwe9G98CkkdqvJB/PhudzH+3Asx/uiPw+TR7VA/dflXyr4T/38Q7M/3BHJItkfx7JnMdzH+/A/Hc3antQJc2Ul5crAJTy8vK63aFvX/X19Z//rPUmb3+1X8HPXlMyfvFv5fBJp0aVpr5Tp04pp06d0ruMBpn9zmYFP3tNmf3O5jpdL1m45scXf6WcOnUqqZ9DuOZkfA6KwiwkSYUsFCU18gjX/NDfP63f/+9zYA/Q2ezfD3z7LWA0AqNGxbxJIBjCo29+AwB44OoeaNOUi2XVVXgQdDKusxE9my1aY2ezJVp0L9bdw9vA7Xafc1kCaWIN6ky25wAwC0lSIQsgNfKIfg639s3CMxoemw2gswmv/nzRRUDz5jFv8up/d2Pn4Qo0z7LhoTG9Elhc8kvmvXXOtnaG9BeUaPFaliCRUqUxyizkSIUsgNTII/o5FBcXa3pszgI7m9GjgQ8/BJ56CnjkkRrfdnkD6PbQuzh00oX5twzCA6N6xqnq1HT06FEAQKtW2q7tQA3DPORgFnIwCzl2796NLl26cBZY3Dmd6rR3ABg7NuZN/rRyJw6ddKF980zcc+X5CSwuNSTjqa9UxjzkYBZyMAs5uBVGonzyCeD1Ah07Aj1qjpY/6fTiqWXbAABzftoPdis3PK0vbjIoC/OQg1nIwSzk4FYYifL+++rnsWNjrl721LJtKHP50Pu8prj1oo4JLi418J2VLMxDDmYhB7OQQ+seoORaCjJRQqHTDaAY218cPOHE8x/vBKBueGoy8sfYEC6Xq9oAQ9IX85CDWcjBLOQIzxzWCnuAYtm4ESguBrKygB/V3NJi5tvfwuMP4pLzW2F0v3Y6FJgabDab3iVQFOYhB7OQg1nIYbVaNT0eG0CxhHt/Ro4Ezvjl336oDH//bDcAYN54bnjaGMEgl2KXhHnIwSzkYBZyaJ0FG0CxnGX398fe3ISQomDcoHwM69oywYWlljRbgUE85iEHs5CDWcihdRZsAJ3p0CH1FJjBoK4DFGXd98ewdMMBGA0GPHnDAJ0KTB1mM3/9JGEecjALOZiFHFpnwdG7Z/rgA/Xz0KFA1MJXStSGpxN/1Bk92uXoUV1K8Xq98Hq9epdBVZiHHMxCDmYhh8/n0/R4bNqeqZbTXx9sPoT/7joKu8WEmdcnz1YHknFdDVmYhxzMQg5mIYfD4dD0eGwARXO71QUQgWoNoGAohCmL1Q1Pf3tVd5yXm7x7WEnCBcZkYR5yMAs5mIUcXAgxnj79VG0E5ecDfU/38vx77V5sPViGphlWTBnLDU+1wgXGZGEecjALOZiFHNwKI56iT39VTW/3+IKY9p/NAIApY3uhWSbXhNAK31nJwjzkYBZyMAs52AMUL4oSc/XnvxTuQtFxJ9o1y8Bvr+quU3Gpie+sZGEecjALOZiFHOwBipdvvwUOHgQyMoArrgAAlLt8eOK9rQCAmdf3hcPKH5eWwq15vrOSgXnIwSzkYBZyaL0lCf+jh4VPf40YAdjtAIBnlm/D8UovurfNxs8v6axjcalJ6xH91DjMQw5mIQezkMNe9b9ZK2wAhZ1x+utImQt/XLEDAPDkDQNgNnHJJK35/X69S6AozEMOZiEHs5BD6yzYAAKAkhJg/Xr18pgxAIDZ72yByxfEhV1aYNygfB2LS13cR00W5iEHs5CDWcihdRZsAAHq6s+KAgwaBLRti++LK/DS6u8BcMPTeDIa2asmCfOQg1nIwSzk0DoLNoCAGqe/Hv/PJgRDCkb3a4cfdc/TsbDUxq5lWZiHHMxCDmYhRyAQ0PR4bAB5vcDHH6uXx47F13uOY8mX+2EwAHNv5Ian8cTBhbIwDzmYhRzMQg6tB0Gzb2/NGqCyEmjTBkr//pENT392USf0bd9M5+JSW2VlZWSRMdIf85CDWcjBLOTgQohaC5/+GjMGK7eXYNX2YljNRsz+ST9960oDXGBMFuYhB7OQg1nIwYUQtRS1+nPommsiG57++spuKGjJX/p44xLzsjAPOZiFHMxCDvYAaWn7dmDvXsBmw+Kc8/HN/q/QxG7BY9f10buytMB3VrIwDzmYhRzMQg72AGmpqvfHd8UIPL5MXfTw4TE90aKJtgOtKDa+s5KFecjBLORgFnKwB0hLVQ2glwaPw569lcjLseOBq3voXFT60Lo1T43DPORgFnIwCzm0boSm7yywEyeAtWtRabZh9lG1i3PGuL7ItFt0Lix9eL1eeL1evcugKsxDDmYhB7OQQ+sc0rcHaOVKIBTC/Ct+jqNOP7rkNcGdl3XVu6q0YjKZ9C6BojAPOZiFHMxCDq2zSN8eoA8/xFFbEzzTZhgA4Ikb+sNiTt8fBxERUTpJ3x6gTz7BE32uRaVixKCOufjpBR30rijtBINBvUugKMxDDmYhB7OQQ+ss0rYBtC9owV+6XQkAeOrGgTAaueFpotlsNr1LoCjMQw5mIQezkEPrLNL2nM8Tfa6D32jGj3u3wYjebfQuJy05nU7NpzVSwzEPOZiFHMxCDpfLpenxRDSAXnzxRRQUFMBut2Po0KFYv379WW//5ptvonv37rDb7ejTpw8++OCDej/mkg5DAACdD+zCzN8+16C6qXGysrK4yJggzEMOZiEHs5BD6yUJdG8ALV68GJMnT8aMGTOwceNG9OvXDyNHjsTRo0dj3n7t2rW4+eabcccdd+Cbb77BuHHjMG7cOGzdurWej2xEb4sHC8uzYeLpL11wk0FZmIcczEIOZiGH1j1xBkVRFE2PWE9Dhw7FBRdcgBdeeAEAEAqFkJ+fj9/85jeYMmVKjduPHz8eTqcT74c3MQVw4YUXon///li4cOE5H6+iogI5OTkw3PAXKLZMzG5+EtMW/Fa7J0R1Fu7O5AqrMjAPOZiFHMxCjuLiYrRp0wbl5eXIzs5u9PF0HQTt8/mwYcMGTJ06NXKd0WjEiBEjsG7dupj3WbduHSZPnlztupEjR2Lp0qUxb3/mIlbl5eUAACXgxUPZx3HXlDuwe/duZGRkwOv1RtYZCAaDsNlscLlcyMzMhNPprPbZ4/HAbDYjFApBURRYLBZ4PB5kZGTUuK3b7YbVakUgEIDBYIDJZILP54PD4ahxW5fLBbvdDr/fD6PRCIPBgEAgALvdXuO2TqczUrfZbIaiKJG63W53zFo8Hg8sFguCwWBc6vb5fDCZTJG6a/sZZmRk4MiRIzCZTMjNzW1Q3V6vN2YtbrcbNpsNfr8/Urff74/5M3S5XHA4HJHs61L3mT9vq9V6zp9huG6z2Vyn7LWuO/p3VlEUhEKhGtm73W643W7k5+c3qm6j0Vin39n6/q3VVndtP28AcflbS8RrRFlZGfx+P9q1a5fWrxGNrVuL14iDBw/CZrOhSZMmaf8aoVXdDX2N2LVrl/r/W6N+G10bQKWlpQgGg8jLy6t2fV5eHnbu3BnzPsXFxTFvX1xcHPP2c+fOxaxZs2p+451JeAbAM6883qDaiYiIKPGOHz+OnJycRh8n5afBT506tVqPUVlZGTp06ICioiJNfoDUcBUVFcjPz8eBAwc06c6kxmEecjALOZiFHOXl5Wjfvj1yc3M1OZ6uDaAWLVrAZDKhpKSk2vUlJSVo3bp1zPu0bt26Xre32Wwx1w7IycnhL7MQ2dnZzEIQ5iEHs5CDWchhNGozf0vXWWBWqxWDBg1CYWFh5LpQKITCwkIMGzYs5n2GDRtW7fYAsHLlylpvT0RERHQm3U+BTZ48GRMmTMDgwYMxZMgQLFiwAE6nExMnTgQA3H777WjXrh3mzp0LALj//vtx6aWX4tlnn8WYMWPwxhtv4Ouvv8bf/vY3PZ8GERERJRHdG0Djx4/HsWPHMH36dBQXF6N///5YsWJFZKBzUVFRte6uiy66CK+//joef/xxPProo+jatSuWLl2K3r171+nxbDYbZsyYweXNBWAWsjAPOZiFHMxCDq2z0H0dICIiIqJE030laCIiIqJEYwOIiIiI0g4bQERERJR22AAiIiKitJN2DaAXX3wRBQUFsNvtGDp0KNavX693SWln7ty5uOCCC9CkSRO0atUK48aNi+zxQvp66qmnYDAYMGnSJL1LSUuHDh3Cz372MzRv3hwOhwN9+vTB119/rXdZaSkYDGLatGno2LEjHA4HOnfujDlz5mi2DxXV7rPPPsPYsWPRtm1bGAyGGnt9KoqC6dOno02bNnA4HBgxYgS+//77ej9OWjWAFi9ejMmTJ2PGjBnYuHEj+vXrh5EjR+Lo0aN6l5ZW1qxZg3vvvRdffPEFVq5cCb/fj6uuugpOp1Pv0tLaV199hb/+9a/o27ev3qWkpZMnT2L48OGwWCz48MMPsX37djz77LNo1qyZ3qWlpXnz5uEvf/kLXnjhBezYsQPz5s3D008/jT/96U96l5bynE4n+vXrhxdffDHm959++mk8//zzWLhwIb788ktkZmZi5MiR8Hg89XsgJY0MGTJEuffeeyNfB4NBpW3btsrcuXN1rIqOHj2qAFDWrFmjdylp69SpU0rXrl2VlStXKpdeeqly//33611S2nnkkUeUiy++WO8yqMqYMWOUX/ziF9Wuu/7665Vbb71Vp4rSEwDlnXfeiXwdCoWU1q1bK88880zkurKyMsVmsyn/93//V69jp00PkM/nw4YNGzBixIjIdUajESNGjMC6det0rIzKy8sBQLMN7qj+7r33XowZM6ba3wcl1nvvvYfBgwfjhhtuQKtWrTBgwAC89NJLepeVti666CIUFhbiu+++AwBs3rwZn3/+OUaNGqVzZelt7969KC4urvZalZOTg6FDh9b7f7nuK0EnSmlpKYLBYGSF6bC8vDzs3LlTp6ooFAph0qRJGD58eJ1X8yZtvfHGG9i4cSO++uorvUtJa3v27MFf/vIXTJ48GY8++ii++uor/Pa3v4XVasWECRP0Li/tTJkyBRUVFejevTtMJhOCwSCeeOIJ3HrrrXqXltaKi4sBIOb/8vD36iptGkAk07333outW7fi888/17uUtHTgwAHcf//9WLlyJex2u97lpLVQKITBgwfjySefBAAMGDAAW7duxcKFC9kA0sGSJUvw73//G6+//jp69eqFTZs2YdKkSWjbti3zSBFpcwqsRYsWMJlMKCkpqXZ9SUkJWrdurVNV6e2+++7D+++/j08//RTnnXee3uWkpQ0bNuDo0aMYOHAgzGYzzGYz1qxZg+effx5msxnBYFDvEtNGmzZt0LNnz2rX9ejRA0VFRTpVlN4eeughTJkyBTfddBP69OmD2267DQ888EBkY27SR/j/tRb/y9OmAWS1WjFo0CAUFhZGrguFQigsLMSwYcN0rCz9KIqC++67D++88w5WrVqFjh076l1S2rryyiuxZcsWbNq0KfIxePBg3Hrrrdi0aRNMJpPeJaaN4cOH11gO4rvvvkOHDh10qii9uVyuahtxA4DJZEIoFNKpIgKAjh07onXr1tX+l1dUVODLL7+s9//ytDoFNnnyZEyYMAGDBw/GkCFDsGDBAjidTkycOFHv0tLKvffei9dffx3vvvsumjRpEjlvm5OTA4fDoXN16aVJkyY1xl5lZmaiefPmHJOVYA888AAuuugiPPnkk7jxxhuxfv16/O1vf8Pf/vY3vUtLS2PHjsUTTzyB9u3bo1evXvjmm28wf/58/OIXv9C7tJRXWVmJH374IfL13r17sWnTJuTm5qJ9+/aYNGkSfv/736Nr167o2LEjpk2bhrZt22LcuHH1eyCNZqoljT/96U9K+/btFavVqgwZMkT54osv9C4p7QCI+fH3v/9d79JIUTgNXkfLli1TevfurdhsNqV79+7K3/72N71LSlsVFRXK/fffr7Rv316x2+1Kp06dlMcee0zxer16l5byPv3005j/IyZMmKAoijoVftq0aUpeXp5is9mUK6+8Utm1a1e9H8egKFzWkoiIiNJL2owBIiIiIgpjA4iIiIjSDhtARERElHbYACIiIqK0wwYQERERpR02gIiIiCjtsAFEREREaYcNICJKWQUFBViwYEHCH9dgMGDp0qUJf1wiqjs2gIio0X7+859XW4b+sssuw6RJkxL2+K+++iqaNm1a4/qvvvoKv/zlLxNWR9iRI0cwatSohD8uEdVdWu0FRkTJxefzwWq1Nvj+LVu21LCauqvvrtRElHjsASIiTf385z/HmjVr8Nxzz8FgMMBgMGDfvn0AgK1bt2LUqFHIyspCXl4ebrvtNpSWlkbue9lll+G+++7DpEmT0KJFC4wcORIAMH/+fPTp0weZmZnIz8/Hr3/9a1RWVgIAVq9ejYkTJ6K8vDzyeDNnzgRQ8xRYUVERrrvuOmRlZSE7Oxs33ngjSkpKIt+fOXMm+vfvj3/+858oKChATk4ObrrpJpw6dapePwOeAiOSjw0gItLUc889h2HDhuGuu+7CkSNHcOTIEeTn56OsrAxXXHEFBgwYgK+//horVqxASUkJbrzxxmr3/8c//gGr1Yr//e9/WLhwIQDAaDTi+eefx7Zt2/CPf/wDq1atwsMPPwwAuOiii7BgwQJkZ2dHHu/BBx+sUVcoFMJ1112HEydOYM2aNVi5ciX27NmD8ePHV7vd7t27sXTpUrz//vt4//33sWbNGjz11FNx+mkRkV54CoyINJWTkwOr1YqMjIxqp4JeeOEFDBgwAE8++WTkukWLFiE/Px/fffcdunXrBgDo2rUrnn766WrHjB5PVFBQgN///ve4++678ec//xlWqxU5OTkwGAxnPfVUWFiILVu2YO/evcjPzwcAvPbaa+jVqxe++uorXHDBBQDUhtKrr76KJk2aAABuu+02FBYW4oknnmjcD4aIRGEPEBElxObNm/Hpp58iKysr8tG9e3cAaq9L2KBBg2rc95NPPsGVV16Jdu3aoUmTJrjttttw/PhxuFyuOj/+jh07kJ+fH2n8AEDPnj3RtGlT7NixI3JdQUFBpPEDAG3atMHRo0fr9VyJSD72ABFRQlRWVmLs2LGYN29eje+1adMmcjkzM7Pa9/bt24drrrkG99xzD5544gnk5ubi888/xx133AGfz4eMjAxN67RYLNW+NhgMCIVCmj4GEemPDSAi0pzVakUwGKx23cCBA/HWW2+hoKAAZnPdX3o2bNiAUCiEZ599Fkaj2mm9ZMmScz7emXr06IEDBw7gwIEDkV6g7du3o6ysDD179qxzPUSUGngKjIg0V1BQgC+//BL79u1DaWkpQqEQ7r33Xpw4cQI333wzvvrqK+zevRsfffQRJk6ceNbGS5cuXeD3+/GnP/0Je/bswT//+c/I4Ojox6usrERhYSFKS0tjnhobMWIE+vTpg1tvvRUbN27E+vXrcfvtt+PSSy/F4MGDNf8ZEJFsbAARkeYefPBBmEwm9OzZEy1btkRRURHatm2L//3vfwgGg7jqqqvQp08fTJo0CU2bNo307MTSr18/zJ8/H/PmzUPv3r3x73//G3Pnzq12m4suugh33303xo8fj5YtW9YYRA2op7LeffddNGvWDD/60Y8wYsQIdOrUCYsXL67Xc3v11VdhMBjqdR8iksegKIqidxFERMlixowZWLNmDVavXq13KUTUCBwDRERUDx9++CFeeOEFvcsgokZiDxARERGlHY4BIiIiorTDBhARERGlHTaAiIiIKO2wAURERERphw0gIiIiSjtsABEREVHaYQOIiIiI0g4bQERERJR22AAiIiKitMMGEBEREaWd/w/9whvMWTSnTQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in np.arange(0,3):\n",
    "    \n",
    "    initial_x = initial_x_3[:,i][:, None]\n",
    "    \n",
    "    x_i = np.zeros_like(initial_x)\n",
    "    x_i = initial_x\n",
    "    X =   initial_x.T;\n",
    "    \n",
    "    # matrix power through iterations\n",
    "    \n",
    "    for x in np.arange(0,num_iterations):\n",
    "        x_i = T@x_i;\n",
    "        X = np.concatenate([X, x_i.T],axis = 0)\n",
    "    \n",
    "    fig, ax = plt.subplots()\n",
    "    \n",
    "    itr = np.arange(0,num_iterations+1);\n",
    "    plt.plot(itr,X[:,0],marker = 'x',color = (1,0,0))\n",
    "    plt.plot(itr,X[:,1],marker = 'x',color = (0,0.6,1))\n",
    "    plt.plot(itr,X[:,2],marker = 'x',color = (0,0.36,0.635))\n",
    "    # decorations\n",
    "    \n",
    "    ax.grid(linestyle='--', linewidth=0.25, color=[0.5,0.5,0.5])\n",
    "    ax.set_xlim(0, num_iterations)\n",
    "    ax.set_ylim(0, 1)\n",
    "    ax.set_xlabel('Iteration, i')\n",
    "    ax.set_ylabel('State')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
